Contents

Conversion

We can apply these in reverse to convert a lambda expression into combinators. Note that the final rule can convert longer expressions - for example, λ x.abcdeg can be converted by setting f = abcde. This will eventually terminate as the third rule reduces the number of applications, so that eventally one of the other rules will take effect and remove the lambdas.

Example

Consider the following lambda expression, which raises one Church numeral to the power of a second: